X‐ RAY SPECTROMETERS

We employ routinely two types of spectrometers: solid‐state detectors and Bragg‐crystal spectrometers for which high transmission can be reached. As a result, both types of detectors are very well adapted for precise measurements of transition intensities. The solid‐state detectors are used to record the total X‐ray emission from 1 to a few tens of keV while the Bragg spectrometer allow performing an efficient zoom of a given X‐ray region over a few 100 eV. In the following, I just give a brief description and discuss the total transmission.

3.3.1 B

,

The first‐generation detectors consist of a rather thick semiconductor crystal (a few mm) so as to detect energetic photon of several tens of keV. A voltage of ~ 1 kV applied across the crystal gives rise to a detection zone and to a thin dead layer. Usually there is also a gold layer acting as the front electrode. The ensemble is connected to a liquid nitrogen cryostat for cooling purpose (Figure 3.6). Typically, a 180 eV FWHM resolution is obtained at 3 keV. The new generation detectors (Figure 3.7) are based on the silicon drift detector (SDD) technique which combines a large sensitive area (the entire wafer is sensitive to radiations, i.e., no dead layer is present) with a small output capacitance due to a sub‐millimeter crystal thickness. A Peltier element cools the crystal down to a working temperature of around −10°C. A FWHM resolution of around 130 eV at 3 keV is reachable. These detectors have to run under good vacuum conditions (10⁻⁷ mbar) and are, consequently, isolated by means of a beryllium window.

Figure 3.6: Picture of one Si(Li) detector connected to its liquid nitrogen cryostat.

Figure 3.7: Picture of one silicon drift detector with its Peltier unit.

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The first‐generation detectors have a large energy range from 1.1 to 70 keV while a detection range from 850 eV to 25 keV is obtained with SDD detectors (but they have a better resolution). The detection efficiency of our detectors has been carefully determined [70] and examples are given in Figure 3.8. We may note that at 3‐5 keV, the efficiencies exceed 80%. In summary, the solid‐state detectors are simple to handle and offer a good compromise between resolution and detection efficiency. In the following, I will name the efficiency of a given detector at the photon energy .

Figure 3.8: Efficiency over the entire energy range of detection for three solid‐

state detectors: green and red for two

SDD detectors and blue for a Si(Li)

detector [70].

b) Bragg crystal spectrometers

Our high‐resolution high‐transmission Bragg‐crystal spectrometers (Figure 3.9) are designed to be very flexible so as to be adaptable to the photon energy to be analyzed and to the resolution needed to separate two close photon energies. A detailed description is presented in [69]. High transmission is achieved by combining a mosaic crystal with a large surface localization detector. Highly oriented pyrolytic graphite (HOPG) crystals well adapted for the analysis of 3‐5 keV X‐rays are used with a mosaic spread (2) of typically 0.4° ‐ 0.6°. With a mosaic crystal, X‐rays of a given energy are reflected (Figure 3.10) within an angular acceptance close to the mosaic spread (much larger than the typical diffraction pattern for perfect

crystal). Figure 3.9: Picture of one Bragg‐crystal

spectrometer.

As a result, the integrated reflectivity ( ) of HOPG leads to transmission of almost one order of magnitude greater than the one obtained with a flat Ge(111) crystal, for instance. We have developed a large (60  60 mm²) home‐made multi‐wire gas detector. This position sensitive detector, running as a proportional counter, is usually filled with either Ar(CH4) or Xe(CH4) at a pressure close to 1 atm and sealed by a thin aluminized Mylar window.

An incident X photon generates, by photoelectric effect, an electron further accelerated towards the anode at 1.6‐

2 kV. It follows an electron avalanche whose opposite induced charge is detected by the cathode. The localization is obtained by charge division and a spatial resolution better than 500 µm can be reached. Characteristic evolutions of the detector efficiency with the photon energy are shown in Figure 3.11. The choice between

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Ar(CH4) and Xe(CH4) depends on the photon energy to be examined. It is clear that Ar(CH4), compared to Xe(CH4), is more suitable to detect the Lyman lines with n > 4 emitted by 13.6 MeV/u argon ions whose energy is around 4.9‐5.1 keV. Indeed, in this range, the L‐edge absorption coefficient of Xe gives rise to a sudden change in the detection efficiency (see red line in Figure 3.11). On the other side, we use Xe(CH4) for the detection of the

~ 3.3 keV krypton Balmer  transitions for an optimal efficiency.

The spectrometers are used in a vertical geometry and the detector is tilted to remove, at first order, the line broadening due to Doppler effect. We also choose an appropriate observation angle in order to be insensitive to the possible polarization of the recorded line intensities (the crystal itself acting as a polarimeter). Moreover, if the two arms of a spectrometer have equal lengths (equal target‐to‐crystal and crystal‐to detector distances), the broadening effects associated with the mosaic spread vanish at first order. Under these conditions, the largest remaining contribution to the resolution comes from the optical quality of the beam. For example, a beam vertically focused down to less than 1 mm and of several mm horizontally leads to a resolution power of about

~ 1500 at 3.8 keV with arms of 1630 mm and a detection performed at = 30°.

Figure 3.10: Schematic behavior of a mosaic crystal reflecting a given photon energy from a punctual source

at a Bragg angle B. Due to the mosaic

structure, the image on the

localization detector is enlarged by a quantity a. The length L1 and L2 are named arms of the spectrometer.

Figure 3.11: Efficiency of our position sensitive detector for two different detection gases with a pressure of 1.15 atm. The detector is sealed with an aluminized Mylar foil (10 µg/cm² of Al and 12 µm of Mylar).

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3.3.2 T

Control and precise knowledge of the global transmission of the detection system is a key parameter to obtain quantitative measurements. A special care is taken to the absolute calibration in terms of efficiency and solid angle for each detector. Indeed, the global detection transmission for a given X‐ray line is given by the following equation:

Eq. 17 ^_ ^_ with ^_

where is the detector efficiency given above (Figure 3.8 for the solid‐state detectors and Figure 3.11 for the Bragg spectrometers).  ⁄ is the relative solid angle in the laboratory frame and 4  ⁄  corresponds to the relativistic correction of solid angles given by the Lorentz transformations. In the case of the ion‐matter interaction, the ion projectile emits X‐rays in flight at a velocity of ⁄ = 0.33 for krypton and 0.17 for argon and the X‐rays are detected at the laboratory angle . Finally, stands for the transmission from an eventual filter placed in front of the detection crystal.

The expression of  ⁄ depends on the collimation system used in front of the collision point. In most cases, we 4

use circular diaphragms to collimate the solid‐state detectors. The relative solid angle becomes simply:

Eq. 18 ^_{ }

if S << D² with S the diaphragm surface and D the distance from the diaphragm to the target. For the measurement linked to the de‐excitation of the long‐lifetime excited states, we have used a slit giving rise to an additional factor explained in §0. For the Bragg spectrometers, the solid angle is proportional to the crystal reflectivity and the crystal width. Finally, we have:

Eq. 19 ^_{  }

with the detector size (60 mm) and L the arm length. I point out here that additional terms have to be taken into account when dealing with the open cell. All the information is given in [69].

In any case, the transmission is always evaluated experimentally. Indeed, either  ⁄ or 4 is determined trough dedicated measurements systematically performed before and after each experiment. Those measurements are usually based on the analysis of the fluorescence yield of solids induced by electron impact.

The composition of those solids is well known, as NaNO3, MgF2, KClAl, Si, CaF2, Sc, and stainless steel. Typical transmissions of ~10^‐5 ‐ 10^‐6 (with accuracy from a few % to 20%) are attained with photons in the 3‐5 keV range.